I did the same job on my 1986 W126 560sec with the hood still on the car.
It can be done pretty easily if you be sure to use the 3M supertrim spray adhesive - It has incredible hold even after a few minutes. Like the other members point out, just carefully cover your car to catch old gunk and new overspray, remove old glue, and go for it! I was able to manage by myself in three hours from start to ready-to-drive.